Overview [1] [2]#
Eigenvector or characteristic vector of a linear transformation is a non-zero vector that only changes by an overall scale when that linear transformation is applied to it.More formally, if T is a linear transformation from a vector space V over a field F into itself and v is a vector in V that is not the zero vector, then v is an Eigenvector of T if T(v) is a scalar multiple of v. This condition can be written as the equation
T(V) =λv
Below Matrix A acts by stretching the vector x, not changing its direction, so x is an Eigenvector of A.
More Information#
There might be more information for this subject on one of the following:- [#1] - Eigenvalues_and_eigenvectors
- based on information obtained 2017-12-28-
- [#2] - Eigenvectors and Eigenvalues - based on information obtained 2017-12-28-